A New Type of Divergence Due to s-d Interaction

概要

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A new type of divergence is found in higher order effects due to the s-d interaction. It is a consequence of the dynamical character of the s-d interaction and cannot be removed even at finite temperatures. The divergent terms are involved firstly in the scattering probability of two electrons, that is, the probability of two successive one-electron scatterings, and secondly in the second order terms of the normalization constant of the perturbed wave function of the total system. It is shown that the way to remove the divergence is to take account of the finite life time of the intermediate states. After the divergence is removed, the magnitude of the divergent terms is comparable to that of the first order terms. The effect of the two-electron scattering on the electrical resistivity of dilute magnetic alloys is investigated and it is found that the resistivity involves a term proportional to T/(αT+T_a), where α~1 and T_a~cε_F/k,c being the concentration of magnetic atoms. This term accounts for an experimental result quite well. Owing to the divergent term in the normalization constant, the magnitude of the localized spin is found to depend on the temperature as S-βT/(αT+T_a), where β~1.
理論物理学刊行会の論文
1965-10-25